The present invention relates to data analysis and in particular is directed to a method for spatial and temporal analysis of nested data for the purpose of deriving critical scales from the data which may be used to evaluate physical systems.
Various techniques for analyzing data are known. These techniques are used to look at data on various levels. For example, data may be analyzed using scales or measures of various sizes. Large scale measures may illustrate visible characteristics on a macroscopic level. Intermediate and small scale analysis may provide information about data which points to a characteristic or characteristics which would not necessarily be apparent. For example, large scale analysis may reveal major features and dimensions, such as, the largest transverse and vertical dimensions. Small scale analysis may provide a more accurate measure of the length of a curve, for example. Intermediate scale analysis may provide information as to the contour or changes in the contour of a curve or surface, which information may be correlated with other known information about such curve and thereby provide a method for categorizing various curves or surfaces in a way which reveals related physical characteristics.
In a physical system, such as a riverbed or channel, the bottom contour, depending upon its shape, may affect the flow and hence the ecology in a variety of ways. The effects may not be known or well understood without a fundamental understanding of the characteristics of the river contour or surface. Also, a comparison of similar river bottom profiles may reveal a common characteristic at one level but may yield an entirely different characteristic at another level, thereby answering questions about diverse behavior of such systems which are not otherwise explainable without deeper analysis.
Some systems measure the perimeter or length of a curve by using scales of reduced size. As the scale length decreases, the perimeter value increases to some limit. However, such measurement systems may have a bias because they begin measuring from the same starting point.
Angle measurements are employed as an alternative approach. Such angle measurements measure an included angle at a given point on the curveat that scale. The supplement of the included angle is a better measure inasmuch as it reveals the degree of change in the curve. The technique does not suffer from the starting point bias of the perimeter length measurement technique discussed above.
Some researchers in geomorphology have asserted that a landscape has characteristic or dominant scales. This is untrue for fractal objects which are defined as having no particular dominant scale at any level. Fractal theory also assumes that for a range of scales the complexity is constant. Thus, it has been difficult to use algorithms dedicated to calculating fractal dimensions for identifying characteristic scales in landscapes, for example, because standard fractal methods are too insensitive to separate dominant scales. Angle measuring has the ability to discern dominant scales unlike the perimeter length measuring technique.
It is therefore desirable to provide techniques for analyzing data by quantifying its nested structure without measurement bias. It is also desirable to derive from the data dominant scales in orthogonal directions in order to further reveal discernible characteristics.